VOL. LXI.] PHIL030PHICAL TRANSACTIONS.'! 193 



Therefore 2 o - 3« - 3« - i x 3" -->--» X 5" -->■-' = 1. . 



Consequently 4y — 3a? — 3z — 1 =0; 2x — y — z=0; 2z — y — I = 0. 

 Therefore x= \0; y=13; 2 = 7; and a'° X i" X c' = (2 X 5 =) 10. 

 Therefore 10a + 13b + 7c = log. of 10, to the form 1. 



Or, since a = -,; o = j^' '^ — sT'' 



Therefore a = 2a — 3p; b = 4p — a — k; c = 2r — q — 3p. 



Consequently p = 3a + 4b + 2c = log. of 2 1 



a = 5a + 6b + 3c = log. of 3 > to the form I. 



R = 7a + 9b + 5c = log. of 5 J 

 Therefore p + r = 10a + 13b + 7c = log. of (2 X 5 =) 10. 

 Andf¥,/a,fR, are the logarithms of 2, 3, 5, respectively, in the scale of loga- 

 rithms whose form is^. 



XLyill. An Inquiry into the Value of the Ancient Greek and Roman Money: 

 By M. Raper, Esq., F. R. S. p. 462. 



In an introduction, Mr. R. enumerates the various writers on the Greek and 

 Roman coins, showing their respective endeavours and labours, and estimating 

 their comparative methods, merits, and defects. In the following discourse, he 

 has collected the most authentic evidence he could find, of the weights of the 

 Attic drachm and the Roman denarius; part of which he had taken from that 

 very valuable publication of the Pembroke collection of coins. In the year 1759, 

 by the favour of the learned and ingenious Dr. Gowin Knight, principal libra- 

 rian of the British Museum, he weighed a considerable number of the most 

 perfect Greek and Roman coins in that noble repository. The scales he used 

 were good workmanship, and his weights were most accurately sized; and, on 

 comparing the Troy ounce he used, with that in the archives of the b. s., in an 

 exquisite balance of Dr. Henry Pemberton, it was found to be -f- of a grain hea- 

 vier; which he therefore allowed for in the following discourse. 



Mr. R. then proceeds to sect. I, on the Attic drachm. And here he observes, 

 that the Greek coins were not only money, but weights also. Thus their drachm 

 was both a piece of money and a weight; their mina was 100 drachms as a 

 sum, and the same number as a weight; and their talent contained 6o minas, or 

 6000 drachms, both by weight and tale. This way of reckoning 100 drachms 

 to the mina, and 6o minas to the talent, was common to all Greece; and where 

 the drachm of one city differed from that of another, their respective talents 

 differed in the same proportion. 



Of all the Greek cities and free states, both in Europe and the lesser Asia, 

 that of Athens was the most famous for the fineness of their silver, and the 

 justness of its weight: Xenophon tells us, that wherever a man carried Attic 

 silver, he would sell it to advantage. And their money deserves our more 



VOL. xiii. C c 



